Search results for "numerical analysis"
showing 10 items of 883 documents
Controllability method for acoustic scattering with spectral elements
2007
We formulate the Helmholtz equation as an exact controllability problem for the time-dependent wave equation. The problem is then discretized in time domain with central finite difference scheme and in space domain with spectral elements. This approach leads to high accuracy in spatial discretization. Moreover, the spectral element method results in diagonal mass matrices, which makes the time integration of the wave equation highly efficient. After discretization, the exact controllability problem is reformulated as a least-squares problem, which is solved by the conjugate gradient method. We illustrate the method with some numerical experiments, which demonstrate the significant improveme…
Line element-less method (LEM) for beam torsion solution (truly no-mesh method)
2008
In this paper a new numerical method for finding approximate solutions of the torsion problem is proposed. The method takes full advantage of the theory of analytic complex function. A new potential function directly in terms of shear stresses is proposed and expanded in the double-ended Laurent series involving harmonic polynomials. A novel element-free weak form procedure, labelled Line Element-Less Method (LEM), has been developed imposing that the square of the net flux across the border is minimum with respect to coefficients expansion. Numerical implementation of the LEM results in systems of linear algebraic equations involving symmetric and positive-definite matrices without resorti…
High-fidelity analysis of multilayered shells with cut-outs via the discontinuous Galerkin method
2021
Abstract A novel numerical method for the analysis of multilayered shells with cut-outs is presented. In the proposed approach, the shell geometry is represented via either analytical functions or NURBS parametrizations , while generally-shaped cut-outs are defined implicitly within the shell modelling domain via a level set function . The multilayered shell problem is addressed via the Equivalent-Single-Layer approach whereby high-order polynomial functions are employed to approximate the covariant components of the displacement field throughout the shell thickness. The shell governing equations are then derived from the Principle of Virtual Displacements of three-dimensional elasticity an…
Guaranteed and computable error bounds for approximations constructed by an iterative decoupling of the Biot problem
2021
The paper is concerned with guaranteed a posteriori error estimates for a class of evolutionary problems related to poroelastic media governed by the quasi-static linear Biot equations. The system is decoupled by employing the fixed-stress split scheme, which leads to an iteratively solved semi-discrete system. The error bounds are derived by combining a posteriori estimates for contractive mappings with functional type error control for elliptic partial differential equations. The estimates are applicable to any approximation in the admissible functional space and are independent of the discretization method. They are fully computable, do not contain mesh-dependent constants, and provide r…
ADI schemes for valuing European options under the Bates model
2018
Abstract This paper is concerned with the adaptation of alternating direction implicit (ADI) time discretization schemes for the numerical solution of partial integro-differential equations (PIDEs) with application to the Bates model in finance. Three different adaptations are formulated and their (von Neumann) stability is analyzed. Ample numerical experiments are provided for the Bates PIDE, illustrating the actual stability and convergence behaviour of the three adaptations.
Dynamic shakedown of structures with variable appended masses and subjected to repeated excitations
1996
Elastic shakedown for discrete, or finite-element discretized, structures subjected to combinations of static and time-variable loads is addressed in the hypothesis of elastic-perfectly plastic material behavior. The static load is conceived as the weight of an additional mass appended to the structure, whereas the time-variable load is conceived as an unknown sequence of excitations belonging to a specified domain, with intervals between subsequent excitations during which the structure is considered as being motionless. It is shown that, in the plane of the static and time-variable load parameters, the structure's dynamic shakedown domain is nonconvex and that its boundary curve generally…
Massive evaluation and analysis of Poincar�� recurrences on grids of initial data: a tool to map chaotic diffusion
2020
We present a novel numerical method aimed to characterize global behaviour, in particular chaotic diffusion, in dynamical systems. It is based on an analysis of the Poincar\'e recurrence statistics on massive grids of initial data or values of parameters. We concentrate on Hamiltonian systems, featuring the method separately for the cases of bounded and non-bounded phase spaces. The embodiments of the method in each of the cases are specific. We compare the performances of the proposed Poincar\'e recurrence method (PRM) and the custom Lyapunov exponent (LE) methods and show that they expose the global dynamics almost identically. However, a major advantage of the new method over the known g…
Revisiting the role of top-down and bottom-up controls in stabilisation of nutrient-rich plankton communities
2019
Understanding the conditions for successful control of phytoplankton by zooplankton in eutrophic ecosystems is a highly important research area with a wide implementation of mathematical modelling. Theoretical models generally predict destabilisation of food webs in eutrophic environments with large-amplitude oscillations of population densities which would eventually result in species extinction. On the other hand, these theoretical predic- tions are often at odds with ecological observations demonstrating stable dynamics even for a high nutrient load. This apparent discrepancy is known in the literature as Rosen- zweig’s “paradox of enrichment”. Recent theoretical works emphasize a crucia…
An advanced numerical treatment of EM absorption in human tissue
2020
The numerical computation of local electromagnetic absorption at points within the human tissue is proposed by avoiding the mesh generation in the problem domain. Recently, meshless numerical methods have been introduced as an alter- native computational approach to mesh based methods. This is an important feature to generate competitive procedure able to provide final evaluations for large data amounts in real time. In this paper the smoothed particle hydrodynamics method is considered to compute the electromagnetic absorption. First experiments are performed in two dimension at single frequencies by considering incident TM plane wave on 2D cylinder simulating a simplified model of human t…
An augmented MFS approach for brain activity reconstruction
2017
Abstract Weak electrical currents in the brain flow as a consequence of acquisition, processing and transmission of information by neurons, giving rise to electric and magnetic fields, which can be modeled by the quasi-stationary approximation of Maxwell’s equations. Electroencephalography (EEG) and magnetoencephalography (MEG) techniques allow for reconstructing the cerebral electrical currents and thus investigating the neuronal activity in the human brain in a non-invasive way. This is a typical electromagnetic inverse problem which can be addressed in two stages. In the first one a physical and geometrical representation of the head is used to find the relation between a given source mo…